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REVIEW 4 major objections 5 minor 52 references

Observations of Carbon Radio Recombination Lines with the NenuFAR telescope. I. Cassiopeia A and Cygnus A

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read NenuFAR observations of Cassiopeia A and Cygnus A yield 398 carbon radio recombination lines and, from their quantum-number-dependent shapes, electron temperatures about 50% lower, densities about 35% lower, and turbulent velocities…

desk verdict NenuFAR's first CRRL paper is a solid instrument validation with real detections and a genuine sensitivity gain, but the claimed quantitative differences from LOFAR are not yet robust because the fitted line intensities are never corrected for the beam dilution the paper itself documents. read the letter →

arxiv 2506.08895 v3 pith:3OL6K3RQ submitted 2025-06-10 astro-ph.GA

Lucie Cros , Antoine Gusdorf , Philippe Salomé , Sergiy Stepkin , Philippe Zarka , Pedro Salas , Alan Loh , Pierre Lesaffre
show 21 more authors
Jonathan Freundlich Marta Alves François Boulanger Andrea Bracco Stéphane Corbel Maryvonne Gerin Javier Goicoechea Isabelle Grenier Jean-Mathias Grie{ss}meier Martin Houde Oleksandr Konovalenko Antoine Marchal Alexandre Marcowith Florent Mertens Frédérique Motte Michel Tagger Alexander Tielens Gilles Theureau Peter Tokarsky Oleg Ulyanov Vyacheslav Zakharenko
This is my paper
classification astro-ph.GA
keywords CarbonradiorecombinationlinesNenuFARCassiopeiaACygnusinterstellarmediumelectrondensitytemperaturelow-frequencyastronomy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper reports observations of carbon radio recombination lines (CRRLs) with the newly commissioned NenuFAR low-frequency telescope, aimed at Cassiopeia A and Cygnus A in the 10–85 MHz band. It detects 398 C$\alpha$ lines (transitions between high Rydberg states with principal quantum numbers $n=426$ to $n=826$) toward Cas A, and stacked fainter lines toward Cyg A, at higher signal-to-noise and spectral resolution than comparable LOFAR data. By fitting how absorption line shapes and integrated intensities vary with principal quantum number, the authors infer the electron temperature $T_e$, electron density $n_e$, radiation field temperature $T_0$, mean turbulent velocity $v_t$, and cloud size $L$ for four line-of-sight clouds. Their derived values differ from LOFAR-based ones: temperatures about 50% lower, densities about 35% lower, and turbulent velocities 10–80% higher. They attribute the differences to beam-size effects, with NenuFAR's larger beam sampling more turbulence and diluting the line-to-continuum ratio against a resolved Galactic background, and conclude that low-frequency CRRLs are sensitive probes that can be mapped over large areas of the Galaxy.

What carries the argument

The central object is the carbon radio recombination line: a transition between adjacent high Rydberg levels ($n+1$ to $n$, here $n=426$ to $826$) seen in absorption against a bright background source at 10 to 85 MHz. Each stacked line is decomposed into a Voigt profile, whose Gaussian (Doppler) width carries the electron temperature $T_e$ and the mean turbulent velocity $v_t$, whose Lorentzian width carries pressure, natural, and radiation broadening set by $T_e$, $n_e$, and the radiation field temperature $T_0$, and whose integrated area carries $T_e$, $n_e$, and cloud length $L$ through departure coefficients. The machinery works because these contributions scale differently with principal quantum number $n$, so the $n$-dependence of the linewidths and integrated areas separates the five physical parameters from a single set of absorption spectra.

What would settle it

Image Cas A and Cygnus A with an interferometer that can synthesize beams from about 5 arcminutes to 3.6 degrees at the same frequencies, and measure the integrated C$\alpha$ line-to-continuum ratio as a function of beam diameter: if the ratio falls as the beam grows, the dilution-by-diffuse-background explanation is confirmed, while if the ratio is beam-independent, the offset instead comes from calibration or from the fitting priors such as the $n>560$ area constraints.

Watch

Extended reading notes

Core claim

Using 71.5 hours on Cassiopeia A and 157.5 hours on Cygnus A in NenuFAR beamforming mode at 95.4 Hz spectral resolution, the authors detect 398 individual C$\alpha$ absorption lines toward Cas A between principal quantum numbers $n=426$ and $n=826$, and obtain eleven usable stacked detections toward Cyg A. They fit Voigt profiles to stacks of 7 to 50 transitions and extract linewidth and integrated line-to-continuum intensity as functions of $n$. Fitting the $n$-dependence with the recombination model of Salgado et al. (2017a,b), they find for the Cas A clouds at $-47$, $-38$, and $0$ km/s respectively: $T_e=45$, $40$, and $52$ K; $n_e=0.027$, $0.025$, and $0.014$ cm$^{-3}$; $v_t=3.3$, $4.7$, and $3.7$ km/s. For the Cygnus A cloud at $3.5$ km/s they find $T_e=77$ K, $n_e=0.018$ cm$^{-3}$, and $v_t=7.9$ km/s. These values imply thermal pressures of a few times $10^3$ K cm$^{-3}$, dominated by turbulent pressure, consistent with standard interstellar medium models. Compared with LOFAR-based estimates for the same sightlines, the NenuFAR fits are on average about 50 percent cooler, about 35 percent less dense, and 10 to 80 percent more turbulent, an offset the paper attributes to NenuFAR's larger beam and the resulting dilution of the line-to-continuum ratio.

Load-bearing premise

The modeling treats each detected velocity component as a single uniform cloud with one electron density and one temperature along the line of sight, seen against an unresolved point-like background; the paper's own comparison shows that line intensities toward Cas A differ by tens of percent between LOFAR and NenuFAR, indicating that this beam-independence condition may not hold and that the fitted $n_e$ and $T_e$ could be biased by dilution.

Editorial extensions

If this is right

  • NenuFAR can routinely detect carbon radio recombination lines across 10–85 MHz: 398 individual C$\alpha$ lines toward Cassiopeia A and usable stacked lines toward Cygnus A, with signal-to-noise about four times higher than LOFAR at matched resolution and about ten times higher when identical transitions are stacked.
  • Resolving three separate velocity components toward Cas A, including the faint 0 km/s component, shows that the new telescope can measure cloud-by-cloud physical conditions rather than a single blended average.
  • The derived pressures, with thermal pressure a few thousand K cm$^{-3}$ and turbulent pressure dominating in all four clouds, match standard expectations for the diffuse neutral interstellar medium, indicating that the fitting procedure returns physically plausible results.
  • If the beam-size interpretation is correct, low-frequency CRRL absorption depends not only on the foreground clouds but also on the beam's overlap with the resolved Galactic background, so future surveys must model beam dilution explicitly when comparing instruments.
  • The $n$-dependence of line shape can now be measured over a wider quantum-number range than before, which sharpens the constraints on where the Doppler-dominated regime transitions to the Lorentzian-dominated regime around $n=580$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If beam dilution is real, earlier LOFAR absorption measurements toward Cas A likely mix true cloud physics with the fraction of background continuum inside the beam, so published $n_e$ and $T_e$ values for these sightlines may need downward revision by tens of percent, and not only for NenuFAR comparisons.
  • Because NenuFAR's beam reaches 3.6 degrees at 10 MHz, the same technique could turn CRRL absorption from a source-by-source probe into a tomographic survey of the diffuse interstellar medium across large areas of the Galactic plane, using many background sources rather than the two brightest ones.
  • The paper reports poor constraints on $T_0$ and $L$ and a multimodal parameter space; a natural extension would be joint fitting of CRRL line shapes with independent tracers such as HI 21-cm absorption, CO, or dust extinction along the same sightlines, which could fix the cloud length and radiation field separately and break the degeneracy.
  • The smaller LOFAR-NenuFAR discrepancy toward the high-latitude Cygnus A sightline than toward the low-latitude Cas A sightline suggests that the diffuse Galactic background itself contributes to CRRL absorption, implying a testable prediction: CRRL optical depth toward extragalactic sources should increase as the telescope beam encompasses more Galactic plane.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents NenuFAR observations of carbon radio recombination lines in absorption towards Cassiopeia A and Cygnus A. After developing a substantial RFI-mitigation and baseline-correction pipeline, the authors detect 398 C-alpha lines toward Cas A between principal quantum numbers n=426 and n=826, stack them into 28 groups, and fit Voigt profiles to three foreground velocity components. For Cyg A they obtain 11 stacked detections toward one component. From the fitted integrated line-to-continuum intensities and line widths (Appendix B), a five-parameter grid search yields electron temperatures, densities, radiation-field temperatures, cloud sizes, and turbulent velocities. The headline result is that the NenuFAR-derived T_e is roughly 50% lower, n_e roughly 35% lower, and v_t 10\u201380% higher than previous LOFAR-based estimates, which the authors attribute to the larger NenuFAR beam sampling a larger volume of diffuse gas.

Significance. If the parameter extraction were robust, this paper would be a significant demonstration that a large single-dish beam can recover CRRL absorption spectra with very high signal-to-noise, and that low-frequency CRRL line shapes are sensitive to the spatial scale of the sampled ISM. The manuscript is honest about many limitations, presents a detailed pipeline, compares directly with LOFAR spectra, and makes the stacked spectra and fitted line parameters available in tables. However, the central quantitative claim\u2014the comparison of T_e, n_e, and v_t with LOFAR\u2014is currently not supported because the forward model omits the beam-dilution effect that the paper itself identifies, and because the fits in the regime that matters most have reduced chi-square values far above one. The paper would be a useful technical and observational benchmark even if the astrophysical comparison were reframed as preliminary.

major comments (4)
  1. [Section 5.1, Eq. (B.4), Fig. 14] The forward model for the integrated line-to-continuum intensity, Eq. (B.4), contains no covering factor or beam-dilution term. The observed A_n is the integral of I_line/I_cont over frequency, so any foreground or background continuum that is not intercepted by the absorbing cloud will multiply the measured A_n by a frequency-dependent factor below unity. The paper's own Fig. 14 shows A_NenuFAR/A_LOFAR dropping to roughly 0.6\u20130.8 at low frequencies toward Cas A, which Sect. 5.1 attributes to dilution by a resolved Galactic background. Because A_n enters the chi-square statistic (Eq. B.16) and scales as n_e^2 T_e^-2.5, an uncorrected 20\u201340% suppression can shift the inferred n_e and T_e at approximately the level of the claimed LOFAR differences. Moreover, the direction of the shift is not trivial: lower observed A_n at fixed T_e would bias n_e downward, but the paper also derives T_e lower than LOFAR, which would increase A_n and require an even larger dilution factor. The paper must either include a dilution/covering-factor parameter in the forward model, calibrate A_n against an external absolute scale, or explicitly restrict the quantitative LOFAR comparison to the high-frequency regime where the dilution is small.
  2. [Section 4.1.2] For n above 560, the fitting procedure imposes hard priors that force the line area of the \u221238 km s^-1 component to be at most one third of the \u221247 km s^-1 area, and the 0 km s^-1 area to be no larger than the \u221238 km s^-1 area. These priors are introduced specifically to manage blending, but they are applied exactly in the regime where the model later fails to reproduce the data (Sect. 4.1.3). The physical parameters reported in Table 2 therefore are not determined from the data alone in this part of the spectrum. The authors should demonstrate that the fitted parameters are robust to relaxing these priors, for example by repeating the fit on a subset of stacks or by leaving the area ratios free with weak logarithmic priors and checking that the results are stable.
  3. [Section 4.1.3, Appendix D] The quoted best fits have reduced chi-square values of about 6.7 for the \u221247 km s^-1 component and 5.3 for the \u221238 km s^-1 component (Figs. D.1 and D.2), while the reported uncertainties are simply the parameter sets within 30% of the optimal chi-square. With chi-square_r >> 1, those uncertainty envelopes and the central values themselves are not statistically meaningful, and the model does not reproduce the observed line-width and intensity curves. This is particularly serious because the paper's LOFAR comparison relies on the exact values of T_e and n_e. The authors should either improve the model (e.g., multi-component or non-uniform clouds) or present the parameter estimates as indicative rather than as measured values.
  4. [Section 4.1.3, Eq. (B.16)] The text states that for n greater than about 600 the measured integrated line-to-continuum intensity collapses because of blending and is not physical, and that the effect 'should not impact the optimisation process.' However, the chi-square definition in Eq. (B.16) includes all stacks used in the analysis, and the grid search presumably uses the same A_n values shown in Fig. 8. If the n>600 points are not excluded from the fit, the optimization is pulled by exactly the regime the authors say cannot be modeled. The manuscript must state clearly whether those points are included or excluded, and, if included, must justify their use despite the acknowledged model failure.
minor comments (5)
  1. [Abstract] The symbol '3 t' appears in the abstract and elsewhere; this should be the mean turbulent velocity v_t (or \sigma_t) with proper mathematical formatting.
  2. [Conclusion] The first cloud toward Cas A is quoted with T_0 = 1200 K in the concluding remarks, while Section 4.1.3 and Table 2 give T_0 = (1700 \u00b1 100) K. Please correct the inconsistency.
  3. [Fig. D.3 caption] The caption labels the panel as 'Cassiopeia A, component \u221247 km s^-1', but the text and panel headers refer to the 0 km s^-1 component; the caption should be corrected.
  4. [Sections 4.1.2 and C.2] The cross-reference 'Table??' appears twice and should point to the actual tables of measured line properties.
  5. [Section 5.1] The discussion of grating lobes is qualitative. Since the authors argue the effect is negligible, a quantitative estimate (e.g., expected source confusion level or a gain pattern calculation) would be more convincing.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the physical-parameter derivation is a standard forward-model fit to measured line shapes; the LOFAR-derived priors are not load-bearing for the central Te/ne/vt constraints.

full rationale

The paper's derivation chain runs from calibrated NenuFAR optical-depth spectra, through Voigt-profile fits of stacked C-alpha lines, to measured integrated line-to-continuum areas A_n and profile widths w_V, and finally to a chi-squared grid search over (T_e, n_e, T_0, v_t, L) using the explicit forward equations B.4-B.10. This is ordinary model fitting, not a self-referential derivation: T_e and n_e are not defined in terms of the fitted A_n and w_V; they are independent grid parameters whose model predictions are compared with the data. The LOFAR-based cloud velocities are used only as line-center priors for masking and deblending (Sect. 3.1.2), and the paper explicitly labels the need for such priors a 'significant caveat'; the line widths and areas that carry the physical constraints remain free fit outputs. The missing beam-dilution term in Eq. B.4, acknowledged in Sect. 5.1, is a potential systematic bias in the inferred T_e and n_e, but it does not make the inference equal to its inputs; an incomplete forward model is a correctness issue, not circularity. Finally, the modeling framework of Salgado et al. (2017a,b) is cited as external support, but the key equations are reproduced in Appendix B, so the derivation is self-contained; no uniqueness theorem or author-specific ansatz is invoked to force the parameter choice. The paper therefore contains no step that is equivalent by construction to its own inputs.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central parameter extraction relies on the Salgado et al. (2017a,b) tabulated model, the assumed homogeneity of clouds, and prior kinematic knowledge from LOFAR. The five physical parameters are all fitted to the same data, and the auxiliary assumptions (spectral index, S/N cap, dust-based L priors) add further degrees of freedom that are not independently verified.

free parameters (7)
  • Electron temperature T_e = 45 K (-47), 40 K (-38), 52 K (0) for Cas A; 77 K for Cyg A
    Fitted via chi2 grid search to observed linewidth and integrated intensity vs. quantum number (Appendix B.2.2).
  • Electron density n_e = 2.7e-2 cm^-3 (-47), 2.5e-2 (-38), 1.4e-2 (0), 1.8e-2 (Cyg A)
    Fitted; partially degenerate with L and T_e, with the degeneracy discussed in Sect. 5.2.
  • Radiation field temperature T_0 = 1700 K (-47), 1200 K (-38), 1000 K (0), 1600 K (Cyg A)
    Poorly constrained; fixed around the optimal value in the refined grid; affects the radiative broadening width.
  • Cloud depth L = 33.0 pc (-47), 20.5 pc (-38), 15.0 pc (0), 8.0 pc (Cyg A)
    Prior from 3D dust maps (Edenhofer et al. 2024); explored +/-10 pc; poorly constrained by the line data.
  • Mean turbulent velocity v_t = 3.3 km/s (-47), 4.7 (-38), 3.7 (0), 7.9 (Cyg A)
    Best-constrained parameter; stable across local minima (Sect. 5.2).
  • Radiation field spectral index alpha = -2.6 (assumed)
    Set following Salgado et al. (2017a) and Salas et al. (2017); not fitted but enters the radiative broadening formula (Eq. B.6).
  • S/N cap for stacking weights = 6
    Lines with S/N>6 are downweighted to S/N=6 to mitigate calibration uncertainty (Sect. 3.3); an ad hoc choice that affects the stacked profiles.
assumptions (6)
  • domain assumption CRRL line formation model of Salgado et al. (2017a,b): departure coefficients b_n and stimulated emission factors beta_n,n' are tabulated and correct for the CNM conditions
    Used to convert observed line areas into n_e, T_e, L via Eq. B.4; the paper does not re-derive or validate the tabulations.
  • domain assumption Carbon is the dominant electron provider and n_CII ~ n_e in the absorbing clouds
    Used to derive EMCII and pressures (Eqs. B.12 to B.15); also implicit in the line formation model.
  • domain assumption Each velocity component is a single homogeneous cloud with constant T_e, n_e, and v_t along the line of sight
    The model fits one set of parameters per cloud; any internal gradients are ignored (Sect. B.1).
  • domain assumption The background source is unresolved and the covering factor is unity for the absorbing clouds
    The optical depth is computed as 1 - I/I_smooth, implicitly assuming the foreground cloud covers the whole background; the paper later questions this for Cas A (Sect. 5.1).
  • ad hoc to paper Expected line velocities and the existence of the clouds are taken from previous LOFAR studies
    The RFI masking (Sect. 3.1.2) and the fitting priors (Sect. 4.1.2) use velocities from Oonk et al. (2017) and Salas et al. (2017).
  • standard math Voigt profile with independent Gaussian (Doppler) and Lorentzian (radiative plus pressure) widths is the correct line shape
    Standard for RRLs; the convolution of Gaussian and Lorentzian is exact for optically thin lines with these broadening mechanisms.

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Cite this review

Pith. "Pith review of Observations of Carbon Radio Recombination Lines with the NenuFAR telescope. I. Cassiopeia A and Cygnus A." pith.science (2026). https://pith.science/paper/3OL6K3RQ

@misc{pith2026250608895,
  author       = {Pith},
  title        = {Pith review of: Observations of Carbon Radio Recombination Lines with the NenuFAR telescope. I. Cassiopeia A and Cygnus A},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3OL6K3RQ}},
  note         = {Machine review of arXiv:2506.08895}
}
read the original abstract

Carbon Radio Recombination Lines (CRRLs) at decametre wavelengths trace the diffuse phase of the interstellar medium (ISM) of the Galaxy. Their observation allows to measure physical parameters of this phase. We observed CRRLs with the recently commissioned New Extension in Nan\c{c}ay Upgrading LOFAR (NenuFAR) telescope towards two of the brightest sources at low-frequency (10-85 MHz): Cassiopeia A and Cygnus A (hereafter Cas A and Cyg A respectively), to measure the density n_e and temperature T_e of electrons in line-of-sight clouds. We used NenuFAR's beamforming mode, and we integrated several tens of hours on each source. The nominal spectral resolution was 95.4 Hz. We developed a pipeline to remove radio frequency interference (RFI) contamination and correct the baselines. We then fitted the spectral lines observed in absorption, associated to line-of-sight clouds. Cas A is the brightest source in the sky at low frequencies and represents an appropriate test bench for this new telescope. On this source, we detected 398 C\alpha lines between principal quantum numbers n=426 and n=826. C\alpha lines towards Cyg A were fainter. We stacked the signal by groups of a few tens of lines to improve the quality of our fitting process. On both sources we reached significantly higher S/N and spectral resolution than the most recent detections by the LOw Frequency ARray (LOFAR). The variation of line shape with n provides constraints on the physical properties of the clouds: T_e, n_e, the temperature T_0 of the radiation field, the mean turbulent velocity v_t and the typical size of the cloud. The NenuFAR observations sample a larger space volume than LOFAR's towards the same sources due to the differences in instrumental beamsizes, and the discrepancies highlight the sensitivity of low-frequency CRRLs as probes of the diffuse ISM, paving the way towards large area surveys of CRRLs in our Galaxy.

Figures

Figures reproduced from arXiv: 2506.08895 by the authors.

Figure 1
Figure 1. Configuration of the NenuFAR telescope. Top panel: lay [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Functional diagram for the processing of L1 level data [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Description of the step 1 of the data processing algorithm (see top part of Fig. 2). The top panel represents the time-frequency [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Description of step 2 of the data processing algorithm (see middle part of Fig. 2). The data presented here corresponds [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Description of the step 3 of data processing (see bottom panel of Fig.2). The black vertical line shows the separation between [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Functional diagrams of the post-processing of the data. The left part of the figure describes the time averaging process [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Post-processing of the data, on the example of Cassiopeia A. The top panel represents the whole spectrum averaged over [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Fit results for the clouds detected towards Cas A and Cyg A. The coloured points correspond to NenuFAR data obtained [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: Overplot of the lines detected towards Cas A (9i, 9ii) and Cyg A (9iii) for LOFAR LBA (black) and NenuFAR (red). The [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Cloud identification for the 0 km s−1 component of Cas A. Top panel: CO spectrum averaged over the largest beam of NenuFAR. The gray line represents the whole spectrum. The coloured part is the sliced used to draw the intensity map in the bottom panel (see Dame et al.…
Figure 13
Figure 13. Figure 13: Frequency dependence of beam sizes for NenuFAR and [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]
Figure 12
Figure 12. Figure 12: Cloud identification for the 3.5 km s−1 component to￾wards Cyg A. Both panels are an overplot of the dust distribu￾tion in gray (Edenhofer et al. 2024) and theoretical LSR veloci￾ties in blue and red contours (Reid et al. 2019). The largest beam of NenuFAR is marked i…
Figure 14
Figure 14. Figure 14: Ratio of line intensities towards Cas A between obser [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]
Figure 15
Figure 15. Figure 15: Illustration of the influence of the parameters [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]

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Works this paper leans on

52 extracted references · 46 canonical work pages

  1. [1]

    Asgekar, A., Oonk, J. B. R., Yatawatta, S., et al. 2013, , 551, L11

    work page 2013

  2. [2]

    M., Lim, P

    Astropy Collaboration , Price-Whelan , A. M., Lim, P. L., et al. 2022, , 935, 167

    work page 2022

  3. [3]

    M., Sip \"o cz, B

    Astropy Collaboration , Price-Whelan , A. M., Sip \"o cz, B. M., et al. 2018, , 156, 123

    work page 2018

  4. [4]

    P., Tollerud, E

    Astropy Collaboration , Robitaille, T. P., Tollerud, E. J., et al. 2013, , 558, A33

    work page 2013

  5. [5]

    2021, , 645, A28

    Bron, E., Roueff, E., Gerin, M., et al. 2021, , 645, A28

    work page 2021

  6. [6]

    & Chengalur, J

    Chowdhury, A. & Chengalur, J. N. 2019, , 486, 42

    work page 2019

  7. [7]

    R., et al

    Cuadrado, S., Salas, P., Goicoechea, J. R., et al. 2019, , 625, L3

    work page 2019

  8. [8]

    2006, Proceedings of the National Academy of Science, 103, 12269

    Dalgarno , A. 2006, Proceedings of the National Academy of Science, 103, 12269

    2006

Show all 52 references
  1. [9]

    M., Hartmann, D., & Thaddeus, P

    Dame, T. M., Hartmann, D., & Thaddeus, P. 2001, , 547, 792

    2001

  2. [10]

    P., et al

    de Gasperin , F., Vink, J., McKean, J. P., et al. 2020, , 635, A150

    2020

  3. [11]

    2024, , 685, A82

    Edenhofer, G., Zucker, C., Frank, P., et al. 2024, , 685, A82

    2024

  4. [12]

    L., Gupta, N., Salas, P., et al

    Emig, K. L., Gupta, N., Salas, P., et al. 2023, , 944, 93

    2023

  5. [13]

    L., Salas, P., de Gasperin , F., et al

    Emig, K. L., Salas, P., de Gasperin , F., et al. 2020, , 634, A138

    2020

  6. [14]

    L., Salas, P., de Gasperin , F., et al

    Emig, K. L., Salas, P., de Gasperin , F., et al. 2019, , 622, A7

    2019

  7. [15]

    Girard, J. N. & Zarka, P. 2023, , 672, A80

    2023

  8. [16]

    P., & Bialy , S

    Godard , B., des For \^e ts , G. P., & Bialy , S. 2024, , 688, A169

    2024

  9. [17]

    Goicoechea, J. R. & Cuadrado, S. 2021, , 647, L7

    2021

  10. [18]

    Gordon, M. A. & Sorochenko, R. L. 2002, Radio Recombination Lines . Their Physics and Astronomical Applications , Vol. 282

    2002

  11. [19]

    Green, D. A. 2014, Bulletin of the Astronomical Society of India, 42, 47

    2014

  12. [20]

    N., Bosman , A

    Heays , A. N., Bosman , A. D., & van Dishoeck , E. F. 2017, , 602, A105

    2017

  13. [21]

    2018, , 615, A129

    Joblin , C., Bron , E., Pinto , C., et al. 2018, , 615, A129

    2018

  14. [22]

    2002, in Le Milieu Interstellaire (EDP Sciences)

    Lequeux, J. 2002, in Le Milieu Interstellaire (EDP Sciences)

    2002

  15. [23]

    2023, , 671, L1

    Liu, X., Liu, T., Shen, Z., et al. 2023, , 671, L1

    2023

  16. [24]

    & Hills, D

    Mebold, U. & Hills, D. L. 1975, , 42, 187

    1975

  17. [25]

    K., Oonk, J

    Morabito, L. K., Oonk, J. B. R., Salgado, F., et al. 2014, , 795, L33

    2014

  18. [26]

    M., & Tielens, A

    Natta, A., Walmsley, C. M., & Tielens, A. G. G. M. 1994, , 428, 209

    1994

  19. [27]

    Oonk, J. B. R., van Weeren , R. J., Salas, P., et al. 2017, , 465, 1066

    2017

  20. [28]

    Oonk, J. B. R., van Weeren , R. J., Salgado, F., et al. 2014, , 437, 3506

    2014

  21. [29]

    Pabst, C. H. M., Goicoechea, J. R., Cuadrado, S., et al. 2024, , 688, A7

    2024

  22. [30]

    Padovani , M., Galli , D., & Glassgold , A. E. 2009, , 501, 619

    2009

  23. [31]

    V., Galli , D., & Caselli , P

    Padovani , M., Ivlev , A. V., Galli , D., & Caselli , P. 2018, , 614, A111

    2018

  24. [32]

    2024, , 685, A74

    Peeters , E., Habart , E., Bern \'e , O., et al. 2024, , 685, A74

    2024

  25. [33]

    & Smits, D

    Prozesky, A. & Smits, D. P. 2018, , 478, 2766

    2018

  26. [34]

    J., Menten, K

    Reid, M. J., Menten, K. M., Brunthaler, A., et al. 2019, , 885, 131

    2019

  27. [35]

    A., Peters, W

    Roshi, D. A., Peters, W. M., Emig, K. L., et al. 2022, , 925, 7

    2022

  28. [36]

    Salas, P., Oonk, J. B. R., Emig, K. L., et al. 2019, , 626, A70

    2019

  29. [37]

    Salas, P., Oonk, J. B. R., van Weeren , R. J., et al. 2017, , 467, 2274

    2017

  30. [38]

    Salas, P., Oonk, J. B. R., van Weeren , R. J., et al. 2018, , 475, 2496

    2018

  31. [39]

    R., Emig, K

    Salas, P., Rugel, M. R., Emig, K. L., et al. 2021, , 653, A102

    2021

  32. [40]

    K., Oonk, J

    Salgado, F., Morabito, L. K., Oonk, J. B. R., et al. 2017 a , , 837, 141

    2017

  33. [41]

    K., Oonk, J

    Salgado, F., Morabito, L. K., Oonk, J. B. R., et al. 2017 b , , 837, 142

    2017

  34. [42]

    J., Lauroesch, J

    Sofia, U. J., Lauroesch, J. T., Meyer, D. M., & Cartledge, S. I. B. 2004, , 605, 272

    2004

  35. [43]

    V., Konovalenko, A

    Stepkin, S. V., Konovalenko, A. A., Kantharia, N. G., & Udaya Shankar, N. 2007, , 374, 852

    2007

  36. [44]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261

    2020

  37. [45]

    K., Bowman, J

    Vydula, A. K., Bowman, J. D., Lewis, D., et al. 2024, , 167, 2

    2024

  38. [46]

    V., Balser, D

    Wenger, T. V., Balser, D. S., Anderson, L. D., & Bania, T. M. 2018, , 856, 52

    2018

  39. [47]

    G., McKee, C

    Wolfire, M. G., McKee, C. F., Hollenbach, D., & Tielens, A. G. G. M. 2003, , 587, 278

    2003

  40. [48]

    Wyrowski, F., Schilke, P., Hofner, P., & Walmsley, C. M. 1997, , 487, L171

    1997

  41. [49]

    Zarka, P., Denis, L., Tagger, M., et al. 2020

    2020

  42. [50]

    2018, , 865, 6

    Zhou, P., Li, J.-T., Zhang, Z.-Y., et al. 2018, , 865, 6

    2018

  43. [51]

    , " * write output.state after.block = add.period write newline

    ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sent...

  44. [52]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.